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Nilai dari x→∞lim​(9x2−12x+7​−3x+7) adalah ....

Pertanyaan

Nilai dari limit as x rightwards arrow infinity of space open parentheses square root of 9 x squared minus 12 x plus 7 end root minus 3 x plus 7 close parentheses adalah .... 

  1. 30 

  2. 18 

  3. 10 

  4. 9 

  5. 5 

Pembahasan:

Untuk menjawab soal limit tak hingga, konsepnya adalah bagi dengan variabel pangkat tertinggi pada fungsi yang diberikan, lalu ingatlah bahwa : a over infinity equals 0 space. space a space adalah space konstanta 

Pada soal diberikan: 

table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as x rightwards arrow infinity of space open parentheses square root of 9 x squared minus 12 x plus 7 end root minus 3 x plus 7 close parentheses end cell row blank equals cell limit as x rightwards arrow infinity of space square root of 9 x squared minus 12 x plus 7 end root minus left parenthesis 3 x minus 7 right parenthesis end cell row blank equals cell limit as x rightwards arrow infinity of space square root of 9 x squared minus 12 x plus 7 end root minus left parenthesis 3 x minus 7 right parenthesis space cross times fraction numerator square root of 9 x squared minus 12 x plus 7 end root plus left parenthesis 3 x minus 7 right parenthesis space over denominator square root of 9 x squared minus 12 x plus 7 end root plus left parenthesis 3 x minus 7 right parenthesis space end fraction end cell row blank equals cell limit as x rightwards arrow infinity of fraction numerator left parenthesis 9 x squared minus 12 x plus 7 right parenthesis minus open parentheses 3 x minus 7 close parentheses squared over denominator square root of 9 x squared minus 12 x plus 7 end root plus left parenthesis 3 x minus 7 right parenthesis space end fraction end cell row blank equals cell limit as x rightwards arrow infinity of fraction numerator left parenthesis 9 x squared minus 12 x plus 7 right parenthesis minus left parenthesis 9 x squared minus 42 x plus 49 right parenthesis over denominator square root of 9 x squared minus 12 x plus 7 end root plus left parenthesis 3 x minus 7 right parenthesis space end fraction end cell row blank equals cell limit as x rightwards arrow infinity of fraction numerator 9 x squared minus 12 x plus 7 minus 9 x squared plus 42 x minus 49 over denominator square root of 9 x squared minus 12 x plus 7 end root plus left parenthesis 3 x minus 7 right parenthesis space end fraction end cell row blank equals cell limit as x rightwards arrow infinity of fraction numerator 30 x minus 42 over denominator square root of 9 x squared minus 12 x plus 7 end root plus left parenthesis 3 x minus 7 right parenthesis space end fraction pangkat space tertinggi space x space end cell row blank equals cell limit as x rightwards arrow infinity of fraction numerator 30 x minus 42 over denominator square root of 9 x squared minus 12 x plus 7 end root plus left parenthesis 3 x minus 7 right parenthesis space end fraction cross times fraction numerator begin display style 1 over x end style over denominator begin display style 1 over x end style end fraction end cell row blank equals cell limit as x rightwards arrow infinity of fraction numerator begin display style fraction numerator 30 x minus 42 over denominator x end fraction end style over denominator begin display style fraction numerator square root of 9 x squared minus 12 x plus 7 end root over denominator square root of x squared end root end fraction end style plus left parenthesis begin display style fraction numerator 3 x minus 7 over denominator x end fraction end style right parenthesis space end fraction end cell row blank equals cell limit as x rightwards arrow infinity of fraction numerator begin display style 30 minus 42 over x end style over denominator begin display style square root of 9 minus 12 over x plus 7 over x squared end root plus left parenthesis 3 minus 7 over x right parenthesis space end style end fraction end cell row blank equals cell fraction numerator begin display style 30 minus 42 over infinity end style over denominator begin display style square root of 9 minus 12 over infinity plus 7 over infinity end root plus left parenthesis 3 minus 7 over infinity right parenthesis space end style end fraction end cell row blank equals cell fraction numerator 30 minus 0 over denominator square root of 9 minus 0 plus 0 end root plus left parenthesis 3 minus 0 right parenthesis end fraction end cell row blank equals cell fraction numerator 30 over denominator square root of 9 plus 3 end fraction end cell row blank equals cell fraction numerator 30 over denominator 3 plus 3 end fraction end cell row blank equals cell 30 over 6 end cell row blank equals 5 end table  

Oleh karena itu, jawaban yang benar adalah E. 

Jawaban terverifikasi

Dijawab oleh:

W. Rohmiyati

Mahasiswa/Alumni Universitas Langlangbuana

Terakhir diupdate 06 September 2021

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